The British Museum is undoubtedly one of the greatest cultural and historical warehouses on earth. You could walk its galleries and rooms every single day of your life and still feel incrementally enriched each time you reached the exit.

But this will never disguise the sense of discomfort and shame that hangs over some of the artefacts on display, such as the Parthenon marbles (even within the name there's shame: the Guardian style guide says this is their official name, not the "Elgin marbles", as some still like to defiantly call them). Even if the labels on the cabinets or walls still refuse to furnish us with all the details, many of us know that the story of how they came to be housed within the museum can often be one of brutality, plunder and deception.

The British Museum is not alone, of course. Just about every major collection in the world will have its own examples of loot on display. (Read Sharon Waxman's Loot: The Battle over the Stolen Treasures of the Ancient World for full details.) We seem to periodically discuss what we are to do about these embarrassments of history, but very little ever gets done other than people posing open-ended, circular questions, such as "who owns history, anyway?" The only restoration of justice that seems to be seriously underway is the return of treasures stolen by the Nazis between 1933 and 1945.

It's nice to see, then, the Chinese reignite this debate with the current fracas over the destiny of two sculptures that were looted from a Beijing palace by the French and British in 1860 during the opium wars before later making their way into the collection of the late fashion designer Yves Saint Laurent. The Chinese government said their sale in an auction last week would threaten the planned expansion of Christie's into China and cause unnecessary diplomatic tension with the French (the auction was held in Paris). Jackie Chan, the Hong Kong-born actor, described the sale as "shameful". Yet, the sale went ahead with the two Qing dynasty bronzes being secured by a telephone bidder for €31m (£27m).

But it now turns out that the mystery bidder was, in fact, an adviser for a Chinese foundation which is seeking to retrieve plundered treasures. Cai Mingchao says he has no intention of paying the money and was simply being "patriotic": "I think any Chinese person would have stood up at that moment. It was just that the opportunity came to me. I was merely fulfilling my responsibilities."

Good for him. It was a rather neat way of making an important point, and if the Parthenon marbles were ever to come up for auction – hypothetical, of course – you can be sure that a Greek patriot would do exactly the same thing.

One of the rather patronising defences often put forward about why such relics should stay put is that they will be better cared for, or reach a wider public, than if they were to be returned "home". The British Museum's website offers a rather woolly statement about why the section of the Parthenon marbles it holds should remain in London:

The current division of the surviving sculptures between museums in eight countries, with about equal quantities present in Athens and London, allows different and complementary stories to be told about them, focusing respectively on their importance for the history of Athens and Greece, and their significance for world culture. This, the Museum's Trustees believe, is an arrangement that gives maximum public benefit for the world at large and affirms the universal nature of the Greek legacy.

The new Acropolis Museum is scheduled to formally open in Athens on 20 June. As is the case with Lord Elgin, it, too, has been accused of cultural vandalism after two historic buildings were demolished to make way for it. Yes, history is a fluid entity of which no single party should hold ownership. But as the ribbon-cutting approaches, expect there to be an ever-increasing volume of discussion about why the marbles held at the British Museum should be returned to Athens and reunited with the section of marbles they were conjoined with for 2,200 years before Lord Elgin's intervention some 200 years ago.

I'm not one who argues that we each need to feel the burden of guilt about the abominable actions of our ancestors, or say sorry on their behalf, as is common these days, but I do think we should right wrongs where possible, and the repatriation of ill-gotten gains is one such example. As the British Committee for the Reunification of the Parthenon Marbles says: "The Greeks have long wanted their Marbles back, but the building of the new Acropolis Museum finally gives them the physical authority to buttress an argument that has too often relied on shrill sentimentalism and unsubtle jingoism. The museum is a provocation, an enticement, a tease. Bernard Tschumi [the Swiss architect] has done everything other than daub slogans on the exterior walls to say to the world at large: 'The Parthenon Marbles belong here, next to the building from which they were taken.'"